1. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Introduction to Binary, Octal and Hexadecimal Numbers Part 3 – Octal Numbers
Thaddeus Konar
11/11/ Slide # 1
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

2. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Octal Integers 1
Just as the each digit (position) in decimal integer is represented by the power of 10, in binary integer each digit represents power of 2, in octal numbers each digit is represented by the power of 8 (Base = 8).
Digits range: 0 -> (Base - 1) Number of values represented by a single digit: Base
Digits range: 0 -> 7 (0,1, 2, 3, 4, 5, 6, 7) Number of values represented by a single digit: 8
11/11/ Slide # 2
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

3. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Octal Integers 2
In the decimal number the digits could be 0,1,2,3,4,5,6,7,8,9. (0 -> Base-1), in binary 0,1 (Base-1), so as you can suspect in octal numbers the digits would be 0,1,2,3,4,5,6,7 (0 -> Base-1).
The single decimal number can represent 10 values, the single binary number can represent only 2 values, and single octal number can represent 8 values.
11/11/ Slide # 3
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

4. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Octal Integers 3
In octal integers Base = 8.
Please recall the formula:
(D0*B0)+(D1*B1)+(D2*B2)+(D3*B3)+…(Dn*Bn)
B0=1, B1=8, B2=64, B3 =512, B4=4096…
Lets look at the octal number 4153
D0=3, D1=5, D2=1, D3=4
11/11/ Slide # 4
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

5. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Octal Integers 4
…4153 means: (3*80)+(5*81)+(1*82)+(4*83) = (3*1)+(5*8)+(1*64)+(4*512) =
Here are the first few octal numbers:
00008 = 010
00048 = 410
00108 = 810
00148 = 1210
00208 = 1610
00018 = 110
00058 = 510
00118 = 910
00158 = 1310
00218 = 1710
00028 = 210
00068 = 610
00128 = 1010
00168 = 1410
00228 = 1810
00038 = 310
00078 = 710
00138 = 1110
00178 = 1510
00238 = 1910
11/11/ Slide # 5
Binary, Octal and Hex Numbers Copyright Thaddeus Konar